Commentary—Interior-Point Methods: Algorithms and Formulations

Semidefinite Programming : Formulations and Primal - Dual Interior - Point Methods

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC’s)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get ar...

Formulations and Algorithms for Routing Problems

Multitrace formulations and Dirichlet-Neumann algorithms

Multitrace formulations (MTF) for boundary integral equations (BIE) were developed over the last few years in [4] and [1, 2] for the simulation of electromagnetic problems in piecewise constant media, see also [3] for associated boundary integral methods. The MTFs are naturally adapted to the developments of new block preconditioners, as indicated in [5], but very little is known so far about s...

Inverse Spanning Tree Problems: Formulations and Algorithms

Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and the deviation of d from c is minimum. In this paper, we consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation between c and d is defin...